Patrick Fritzsch

The strange quark mass and Lambda parameter of two flavor QCD

We complete the non-perturbative calculations of the strange quark mass and the Lambda parameter in two flavor QCD by the ALPHA collaboration. The missing lattice scale is determined via the kaon decay constant, for whose chiral extrapolation complementary strategies are compared. We also give a value for the scale r0 in physical units as well as an improved determination of the renormalization constant ZA.

The gradient flow coupling in the Schrödinger functional

A bstractWe study the perturbative behavior of the Yang-Mills gradient flow in the Schrödinger Functional, both in the continuum and on the lattice. The energy density of the flow field is used to define a running coupling at a scale given by the size of the finite volume box. From our perturbative computation we estimate the size of cutoff effects of this coupling to leading order in perturbation theory. On a set of Nf = 2 gauge field ensembles in a physical volume of L ~ 0.4 fm we finally demonstrate the suitability of the coupling for a precise continuum limit due to modest cutoff effects and high statistical precision.

Decay constants of B-mesons from non-perturbative HQET with two light dynamical quarks

Abstract We present a computation of B-meson decay constants from lattice QCD simulations within the framework of Heavy Quark Effective Theory for the b-quark. The next-to-leading order corrections in the HQET expansion are included non-perturbatively. Based on N f = 2 gauge field ensembles, covering three lattice spacings a ≈ ( 0.08 – 0.05 ) fm and pion masses down to 190 MeV , a variational method for extracting hadronic matrix elements is used to keep systematic errors under control. In addition we perform a careful autocorrelation analysis in the extrapolation to the continuum and to the physical pion mass limits. Our final results read f B = 186 ( 13 ) MeV , f B s = 224 ( 14 ) MeV and f B s / f B = 1.203 ( 65 ) . A comparison with other results in the literature does not reveal a dependence on the number of dynamical quarks, and effects from truncating HQET appear to be negligible.

Parameters of heavy quark effective theory from N-f=2 lattice QCD

A bstractWe report on a non-perturbative determination of the parameters of the lattice Heavy Quark Effective Theory (HQET) Lagrangian and of the time component of the heavy-light axial-vector current with Nf = 2 flavors of massless dynamical quarks. The effective theory is considered at the 1/mh order, and the heavy mass mh covers a range from slightly above the charm to beyond the beauty region. These HQET parameters are needed to compute, for example, the b-quark mass, the heavy-light spectrum and decay constants in the static approximation and to order 1/mh in HQET. The determination of the parameters is done non-perturbatively. The computation reported in this paper uses the plaquette gauge action and two different static actions for the heavy quark described by HQET. For the light-quark action we choose non-perturbatively O(a)-improved Wilson fermions.

Non-perturbative improvement of quark mass renormalization in two-flavour lattice QCD

We non-perturbatively determine the renormalization constant and the improvement coefficients relating the renormalized current and subtracted quark mass of (quenched) valence quarks propagating in a sea of O(a) improved two massless quarks. We employ the Schrödinger functional scheme and fix the physical extent of the box by working at a constant value of the renormalized coupling. Our calculation yields results which cover two regions of bare parameter space. One is the weak-coupling region suitable for volumes of about half a fermi. By making simulations in this region, quarks as heavy as the bottom can be propagated with the full relativistic QCD action and renormalization problems in HQET can be solved non-perturbatively by a matching to QCD infinite volume. The other region refers to the common parameter range in large-volume simulations of two-flavour lattice QCD, where our results have particular relevance for charm physics applications.

Non-perturbative renormalization of the static axial current in two-flavour QCD

We perform the non-perturbative renormalization of matrix elements of the static-light axial current by a computation of its scale dependence in lattice QCD with two flavours of massless O(a) improved Wilson quarks. The regularization independent factor that relates any running renormalized matrix element of the axial current in the static effective theory to the renormalization group invariant one is evaluated in the Schrodinger functional scheme, where in this case we find a significant deviation of the non-perturbative running from the perturbative prediction. An important technical ingredient to improve the precision of the results consists in the use of modified discretizations of the static quark action introduced earlier by our collaboration. As an illustration how to apply the renormalization of the static axial current presented here, we connect the bare matrix element of the current to the Bs-meson decay constant in the static approximation for one value of the lattice spacing, a ≈ 0.08fm, employing large-volume Nf = 2 data at � = 5.3.

The b-quark mass from non-perturbative

Abstract We report our final estimate of the b-quark mass from N f = 2 lattice QCD simulations using Heavy Quark Effective Theory non-perturbatively matched to QCD at O ( 1 / m h ) . Treating systematic and statistical errors in a conservative manner, we obtain m ¯ b MS ¯ ( 2 GeV ) = 4.88 ( 15 ) GeV after an extrapolation to the physical point.

N_f=2

We discuss the determination of the strong coupling α_{MS[over ¯]}(m_{Z}) or, equivalently, the QCD Λ parameter. Its determination requires the use of perturbation theory in α_{s}(μ) in some scheme s and at some energy scale μ. The higher the scale μ, the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the Λ parameter in three-flavor QCD, we perform lattice computations in a scheme that allows us to nonperturbatively reach very high energies, corresponding to α_{s}=0.1 and below. We find that (continuum) perturbation theory is very accurate there, yielding a 3% error in the Λ parameter, while data around α_{s}≈0.2 are clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.

Heavy Quark Effective Theory at

The 2012 PDG reports a tension at the level of

O(1/m_h)

3 \sigma